You are here: MIMS > research > applied mathematics > scientific computing
MIMS

Research in Scientific Computing

The members of the Scientific Computing group are interested in the numerical simulation of physical processes, such as fluid flow, heat and mass transfer, and large deformation of solid bodies and particularly the interaction between such processes. Typical research projects start with the development of suitable mathematical models for the physical system; this is followed by the formulation of appropriate discretisations for the governing equations and the design of efficient methods for their numerical solution on state-of-the-art computers. Computational studies are often complemented by asymptotic analyses, and many projects involve collaborations with experimentalists (particularly at the MCND). The development and optimisation of numerical methods frequently involves close interactions with members of the Numerical Analysis group, particularly the Finite Element group.

Current work includes the development of an object-oriented finite element library (oomph-lib) for the simulation of nonlinear multi-physics problems, such as large-displacement fluid-structure interaction problems.

As a representative example, the figure below shows some recent results from the numerical simulation of "pulmonary airway closure", a surface-tension-driven, fluid-elastic instability of the lung's liquid lining that leads to the occlusion of the airway with a liquid bridge. The figures show different stages of this instability:

Numerical simulation of pulmonary airway closure. The shaded volume represents the fluid; the inner surface is the air-liquid interface and the outer surface is the airway wall (only 5/6 of the fluid layer are shown).

Initially, a thin liquid film lines the axisymmetric airway wall (top left); a primary axisymmetric instability causes the redistribution of fluid along the airway (top right); surface-tension creates a strong compressive load on the airway wall in the region where the film thickness increases. When this compression becomes sufficiently large, the airway buckles non-axisymmetrically (bottom left) and ultimately becomes completely occluded by the fluid (bottom right). The results were obtained from a finite-element-based solution of the unsteady, 3D Navier-Stokes equations (describing the fluid flow), coupled to the equations of large-displacement shell theory (describing the deformation of the elastic airway wall).

Members of staff involved

NAME Title EMAIL @manchester.ac.uk PHONE LOCATION
Hazel Andrew Dr Andrew.Hazel 0161 27 55809 Room 2.213
Heil Matthias Prof. Matthias.Heil 0161 27 55808 Room 2.224
Powell Catherine Dr C.Powell 0161 30 63688 Room 1.124
Silvester David Prof. David.Silvester 0161 30 63656 Room 1.117